You have a shuffled deck of three cards: 2, 3, and 4, and you deal out the three cards. Let Ei denote the event that ith card dealt is even numbered.

(a) What is P[E2|E1], the probability the second card is even given that the first card is even?

(b) What is the conditional probability that the first two cards are even given that the third card is even?

(c) Let Oi represent the event that the ith card dealt is odd numbered. What is P[E2|O1], the conditional probability that the second card is even given that the first card is odd?

(d) What is the conditional probability that the second card is odd given that the first card is odd?